Ballistic heat transfer in a one-dimensional crystal with long-range interactions

Raisa V. Rubinova, Olga S. Loboda, Anton M. Krivtsov

Author details

Raisa V. Rubinova
Fraunhofer Institute for Integrated Circuits IIS, Germany, 91058 (work was performed while with Peter the Great St. Petersburg Polytechnic University)
Olga S. Loboda
Peter the Great St. Petersburg Polytechnic University (SPbPU), Russian Federation, 195251; Institute for Problems in Mechanical Engineering, Russian Federation, 199178
Anton M. Krivtsov
Peter the Great St. Petersburg Polytechnic University (SPbPU), Russian Federation, 195251; Institute for Problems in Mechanical Engineering, Russian Federation, 199178

https://doi.org/10.15593/perm.mech/2023.5.07

Non-stationary thermal processes in low-dimensional structures are considered. A previously developed analytical model of ballistic heat transfer is used. The paper focuses on a one-dimensional harmonic crystal with non-nearest neighbour interactions. The coupling forces correspond to the case of a crystal with dipole interactions between the particles. The number of interacting neighbour varies. The dependence of thermal processes on the number of interacting particles has been studied. To describe the evolution of the initial thermal disturbance, an analysis of the dispersion characteristics and group velocities was carried out. It is shown that if only the nearest neighbors are considered, the maximum group velocity will be 78% of the maximum group velocity achieved when considering an infinite number of neighbors. The fundamental solution to the heat propagation problem has been constructed. A solution is obtained for the case of an initial disturbance in the form of a rectangular pulse. An assessment of the influence of neighbours on the rate of heat propagation and on the shape of the heat front was made. The dynamics of changes in wave intensity coefficients depending on the number of neighbors has been revealed. The thermal front is shown to propagate with a finite velocity equal to the maximum group velocity, which increases as more interactions are taken into account. However, the wave intensity factor decreases when the considered neighbours increase. The results obtained in this article aim to describe the heat transfer process in high-purity long-range crystals, such as dipole crystals. The results also help to estimate the error of com- puter modelling of such processes, since for numerical calculations it is necessary to limit the number of interacting particles.

Keywords

harmonic crystallong-range interactionnonstationary heat processesheat wavesfundamental solutiondipole interaction.

БАЛЛИСТИЧЕСКИЕ ПРОЦЕССЫ РАСПРОСТРАНЕНИЯ ТЕПЛА В ОДНОМЕРНОМ КРИСТАЛЛЕ С ДАЛЬНОДЕЙСТВИЕМ

В работе исследуются нестационарные тепловые процессы в низкоразмерных структурах и изучается влияние на эти процессы неближайших соседей. Используется ранее разработанная аналитическая модель баллистического теплообмена. Рассматривается одномерный гармонический кристалл с учетом влияния дальнейших соседей. Силы связи соответствуют случаю кристалла с дипольным взаимодействием между частицами. Количество взаимодействующих соседей варьируется. Исследована зависимость тепловых процессов от числа взаимодействующих частиц. Для описания эволюции начального теплового возмущения проведен анализ дисперсионных характеристик и групповых скоростей. Показано, что если учитывать только ближайших соседей, то максимальная групповая скорость будет составлять 78 % от максимальной групповой скорости, достигаемой при рассмотрении бесконечного числа соседей. Построено фундаментальное решение задачи о распространении тепла. Получено решение для случая начального возмущения в виде прямоугольного импульса. Сделана оценка влияния числа соседей на форму и скорость распространения теплового фронта. Выявлена динамика изменения коэффициентов интенсивностей волн в зависимости от числа соседей. Показано, что тепловой фронт распространяется с конечной скоростью, равной максимальной групповой скорости, которая увеличивается по мере того, как учитывается больше взаимодействий. Однако коэффициент интенсивности волн уменьшается с ростом учитываемых соседей. Полученные в статье результаты предназначены для описания процесса теплообмена в высокочистых кристаллах с дальнодействием, таких как дипольные кристаллы. Результаты также помогают оценить по- грешность компьютерного моделирования таких процессов, так как для численных расчетов необходимо ограничивать число взаимодействующих частиц.

Ключевые слова

гармонический кристаллдальнодействиенестационарные тепловые процессытепловые волныфундаментальное решениедипольное взаимодействие.

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Article information

Published: 4 December 2023
Issue date: 4 December 2023
Issue: No. 5 (2023)